|  SEP 1983

Further Analysis of Triple Exponential Smoothing by ANTHONY WARREN, Ph.D./Technical Analysis staff writer

Further Analysis of Triple Exponential Smoothing by ANTHONY WARREN, Ph.D./Technical Analysis staff writer In the July issue of Technical Analysis, J. Hutson presented a method of using triple exponential smoothing (TRIX) as a trading oscillator and supplied a BASIC routine for calculating TRIX plots. In this article we present a precise method for selecting the TRIX alpha constant using Fourier Spectrum analysis and show how to use historical price data for selecting buy and sell indicators. In Part I we discuss choosing an optimal alpha value using Fourier Analysis and the author's alpha selection curve. Readers unfamiliar with Fourier Analysis and its uses in designing trading systems (as explained in the author's January and May articles) may skip this section and proceed directly to Part II. In Part II we discuss selection of significance bands and trend reversal constants for optimal selection of buy and sell indicators. Part I: TRIX Spectrum Analysis and Alpha Selection The TRIX oscillator consists of applying triple exponential filtering (filtering the input data three times) followed by output data differencing, i.e., taking the difference between the current filtered value and the previous day filtered value. The idea behind this method is that the differencing operation attenuates very long data cycles (low frequencies), and the triple exponential filter removes the daily trading noise which is predominant at short cycles (high frequencies). The resultant filtered data only contains the cycles of interest for trading. The differencing operation unfortunately has the effect of increasing the power in all higher frequency components, and thus triple exponential filtering is required in order to adequately suppress these noise components. (Double exponential filters do not provide enough smoothing to eliminate all the noise components.) In principle, we want to choose the TRIX alpha constant to retain all the data cycles of interest and to reject all of the high frequency noise components. Fourier Analysis of historic price data allows us to do this.

by Anthony W. Warren, Ph.D.